(I) 3, 13, 23, 43, 53, 63, ...

That's the arithmetic sequence that has first term a1=3
and common difference d=10.  So we use the formula for the nth
term:

an = a1+(n-1)d

Substituting a1=3, d=10.

The general term is

an = 3+(n-1)(10)

an = 3+10(n-1)

an = 3+10n-10

an = 10n-7    <--general term

Substituting n=25

a25 = 10(25)-7

a25 = 250-7

a25 = 243     <--25th element

-------------------------

(II) 3, 8, 13, 18, 23, 27, ...

That's the arithmetic sequence that has first term a1=3
and common difference d=5.  

Do it the same way.

-------------------------

(III) 1, 3, 5, 7, 9, 11, 13, 15, ...

That's the arithmetic sequence that has first term a1=1
and common difference d=2.  

Do it the same way.

Edwin